SchoolPhysics: Stability of a bicycle

SchoolPhysics Online, by Keith Gibbs, considers itself to be “an invaluable resource base for all 11 to 19 year old physics students and their teachers.” That may be true, unless those students and their teachers wish to learn about why a bicycle is easier to balance when it is moving forward than when it is stationary.

Unless the bicycle is free falling in the vacuum of space, it will experience externally applied moments, and angular momentum will not be conserved.

Mr. Gibbs explains further with these two nuggets:

Now a stationary bike wheel has no angular momentum and so does not need a force to change the direction of the axle – in other words the bike can easily fall over.

However the rotating bike wheel has angular momentum and so requires a force, in some cases a considerable one, to make the axle of the wheel change direction, and so the wheel stays upright.

Of course, it is not a force that can cause the axle of a wheel to change direction, but a couple or moment, and the existence of angular momentum is not what necessitates a couple or moment in order to change the direction of an axle, just a non-zero mass moment of inertia.

Then, if the wheel is spinning, so that it also has angular momentum about its axle, the axle does not resist changing direction in response to an applied moment, it just changes direction in a different way, by precessing about an axis at right angles to both the axle and the applied moment. If it is not free to precess about this third axis, as is the case of the rear wheel if the tires are in contact with the ground and the front wheel if the steering is locked, then it will respond to the applied moment as though it were not spinning at all.